x-y-7-x-3-y-3-133-x-y-

Question Number 217659 by ArshadS last updated on 17/Mar/25

x + y = 7 \land x^{3} + y^{3} = 133; x, y = ?

Answered by Frix last updated on 17/Mar/25

2 + 5 = 7

8 + 125 = 133

Answered by Rasheed.Sindhi last updated on 18/Mar/25

Using

a^{3} + b^{3} = (a + b) (a^{2} - ab + b^{2})

x + y = 7 \land x^{3} + y^{3} = 133; x, y = ?

(x + y) (x^{2} - x y + y^{2}) = 133

(7) (x^{2} - x y + y^{2}) = 133

x^{2} - x y + y^{2} = 133 / 7 = 19

{(x + y)}^{2} - 3 x y = 19

7^{2} - 3 x y = 19

3 x y = 49 - 19 = 30

x y = 10

y = 10 / x

x + \frac{10}{x} = 7

x^{2} - 7 x + 10 = 0

(x - 2) (x - 5) = 0

x = 2, 5

y = \frac{10}{2}, \frac{10}{5} = 5, 2

(x, y) = {(2, 5), (5, 2)}

Answered by Rasheed.Sindhi last updated on 18/Mar/25

Using

a^{3} + b^{3} + c^{3} - 3 abc

= (a + b + c) (a^{2} + b^{2} + c^{2} - ab - bc - ca)

x + y = 7 \land x^{3} + y^{3} = 133; x, y = ?

x^{3} + y^{3} + 1 - 3 x y = 133 + 1 - 3 x y

(x + y + 1) (x^{2} + y^{2} + 1 - (x y + y + x)) = 134 - 3 x y

(7 + 1) ({(x + y)}^{2} - 3 x y + 1 - (x + y)) = 134 - 3 x y

8 (7^{2} - 3 x y + 1 - 7) = 134 - 3 x y

8 (43 - 3 x y) = 134 - 3 x y

344 - 24 x y = 134 - 3 x y

21 x y = 210

x y = 10

x + y = 7

(x, y) \in {(2, 5), (5, 2)

Commented by ArshadS last updated on 19/Mar/25

G r a t e f u l f o r m u l t i p l e s o l u t i o n s .

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